Order(N) tight-binding molecular dynamics (TBMD) simulations are performed to investigate the thermal stability of ( 10, 10) metallic single-walled carbon nanotubes (SWCNTs). Periodic boundary conditions (PBCs) are applied in the axial direction. The velocity Verlet algorithm along with the canonical ensemble molecular dynamics (NVT) is used to simulate the tubes at the targeted temperatures. The effects of slow and rapid temperature increases on the physical characteristics, structural stability and the energetics of the tube are investigated and compared. Simulations are carried out starting from room temperature and the temperature is raised in steps of 300 K. The stability of the simulated metallic SWCNT is examined at each step before it is heated to higher temperatures. The first indication of structural deformation is observed at 600 K. For higher heat treatments the deformations are more pronounced and the bond-breaking temperature is reached around 2500 K. Gradual ( slow) heating and thermal equilibrium ( fast heating) methods give the value of radial thermal expansion coefficient in the temperature range between 300 and 600 K as 0.31 x 10(-5) and 0.089 x 10(-5) K-1, respectively. After 600 K, both methods give the same value of 0.089 x 10(-5) K-1. The ratio of the total energy per atom with respect to temperature is found to be 3 x 10(-4) eV K-1.